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Simplifying -8(v + 3) + 3v + 7 = 6v + 12 Reorder the terms: -8(3 + v) + 3v + 7 = 6v + 12 (3 * -8 + v * -8) + 3v + 7 = 6v + 12 (-24 + -8v) + 3v + 7 = 6v + 12 Reorder the terms: -24 + 7 + -8v + 3v = 6v + 12 Combine like terms: -24 + 7 = -17 -17 + -8v + 3v = 6v + 12 Combine like terms: -8v + 3v = -5v -17 + -5v = 6v + 12 Reorder the terms: -17 + -5v = 12 + 6v Solving -17 + -5v = 12 + 6v Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-6v' to each side of the equation. -17 + -5v + -6v = 12 + 6v + -6v Combine like terms: -5v + -6v = -11v -17 + -11v = 12 + 6v + -6v Combine like terms: 6v + -6v = 0 -17 + -11v = 12 + 0 -17 + -11v = 12 Add '17' to each side of the equation. -17 + 17 + -11v = 12 + 17 Combine like terms: -17 + 17 = 0 0 + -11v = 12 + 17 -11v = 12 + 17 Combine like terms: 12 + 17 = 29 -11v = 29 Divide each side by '-11'. v = -2.636363636 Simplifying v = -2.636363636
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